Multiple choice

If difference of the roots of the equation $x^2 - px + 8 = 0$ is $2$, then $p$ equals

  1. $\pm 6$
  2. $\pm 2$
  3. $2, -6$
  4. $6, 2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the roots be alpha and beta. alpha + beta = p and alpha * beta = 8. Given |alpha - beta| = 2. Using (alpha - beta)^2 = (alpha + beta)^2 - 4*alpha*beta, we get 2^2 = p^2 - 4(8), so 4 = p^2 - 32. Thus p^2 = 36, meaning p = +/- 6.

AI explanation

For the quadratic equation x squared minus px plus 8 equals 0, the sum of the roots is p and the product is 8. The difference of the roots squared equals the sum of the roots squared minus 4 times the product of the roots. Substituting the known values gives 2 squared equals p squared minus 32. Solving p squared equals 36 gives p equals positive 6 or negative 6.

Keep practicing — related questions